Generative AI for Bayesian Computation.

Area of Science:

• Computational Statistics
• Machine Learning
• Bayesian Inference

Background:

• Traditional Bayesian inference methods can be computationally intensive.
• Approximate Bayesian Computation (ABC) and Generative Adversarial Networks (GANs) have limitations in density estimation and feature selection.
• Likelihood-free models pose challenges for standard Bayesian analysis.

Purpose of the Study:

• To introduce Generative Bayesian Computation (GBC) as a simulation-based approach for Bayesian inference.
• To leverage Quantile Neural Networks (QNNs) for mapping base distributions to posterior distributions.
• To demonstrate the method's applicability to both parametric and likelihood-free models.

Main Methods:

• Training a Quantile Neural Network (QNN) to approximate posterior distributions from samples.
• Recasting inference as a supervised learning problem using a generated dataset of parameter-output pairs.
• Utilizing dimensionality-reducing summary statistics for feature selection in a density-free manner.

Main Results:

• The GBC methodology was successfully applied to the normal-normal learning model.
• The approach was validated on real-world datasets for traffic speed modeling and satellite drag surrogate modeling.
• Performance was compared favorably against state-of-the-art methods.

Conclusions:

• Generative Bayesian Computation with QNNs offers a flexible and efficient alternative for Bayesian inference.
• The density-free and feature-selection capabilities of quantile architectures provide significant advantages.
• The method shows promise for complex parametric and likelihood-free modeling tasks.